Educational attainment and intergenerational mobility: A polygenic score analysis

Aldo Rustichini, William G. Iacono, James J. Lee, and Matt McGue| Journal of Political Economy 2023 131:10, 2724-2779

伊藤成朗

Summary of this paper

  • US Minnesota Twin Study Sample
  • Build a genetic model (with better genetics foundation than ad hoc econ standard model)
  • Intergenerational elaciticity of income is predicted and estimated to be larger in genetic models
  • Empirical pathway: Through parental education and incomes, parental PGS has no direct effect
  • Parental PGS ⇏ educational attainment, after controling for parental education and incomes

Background

SNP, polygenic score

Genome

 

Double helix and rung

Double helix and rung

 

SNP

SNP
.
└── Chromosome
    └── DNA
        └── Gene
            └── Genome

  • Chromosomes: 1/2 each from both parents
  • DNA: Rolled up and shapes like an X
  • Gene: DNA segments
  • Genome: 3 billion nucletiodes (letters)
    • Letter sequence = genome sequence
    • 1.5 billion base pairs (alelles, 対立遺伝子)
  • Base pairs differ between people in less than 1% (15 million) locations
  • Single-nucleotide polymorphism (SNP) = such location
    • 2 chromosomes per person → AT-AT, GC-GC, AT-GC or 0, 2, 1 (reference = GC)

Twin studies

  • Estimate how much genetic factors collectively matter for explaining variations of a trait
    • Collectively: Unit = group level aggregation
    • Explaining variations: Variance decomposition
  • Do not reveal which SNP is correlated

Genome wide association studies (GWASs)

  • Collect \(M\) observable (?) SNPs of (family \(i\)) individual \(j\).

Regress outcome \(y^{i}_{j}\) on \(m\)-th SNP for all \(m=1, \dots, M\):

\[ y^{i}_{j} = \beta_{m}SNP^{i}_{jm}+\epsilon^{i}_{jm}, \quad m=1,\dots,M. \]

Remember:

  • Environment is endogenous to the trait in SNP regressions
    • \(\cov[SNP^{i}_{jm}, \epsilon^{i}_{jm}]> 0\): Parents see traits which may be correlated with \(SNP^{i}_{jm}\) and decide on investments
    • Estimated \(\beta_{m}\) should be upwardly biased
  • No attempts to correct for this

Polygenic score = Predicted outcomes based on all relevant SNPs

\[ PGS^{i}_{j}=\sum_{m=1}^{M}\tilde{\beta}_{m} SNP^{i}_{jm} \]

  • Use Bayesian LDpred procedure to correct for correlations in \(\tilde{\beta}_{m}\)
    • Barth, Papageorge, and Thom (2020) follow the convention and use all SNPs: Better out-of-sample results than using only SNPs with genome-wide significance \(p\) value \(< 5*10^{-8} =\) .0000005%
  • PGS is considered to be a predictor of individual fixed effects
    • Edu attainment SNPs \(\SIM\) biological process of brain development, cognition (Okbay et al. 2016; Lee et al. 2018)
    • Edu attainment SNPs \(\SIM\) cognition SNPs (Okbay et al. 2016)
    • HRS sample: cov[EA score, schooling years] / variance[schooling years] = 10.6%

Intergenerational skill formation

  • Becker and Tomes (1979): AR(1)
  • Goldberger (1989): Weighted average of all ancestors
  • Both are incorrect, this paper shows there exists an invariant (stable) mapping father genotype distribution × mother genotype distribution \(\to\) child genotype distribution, so skill formation depends on parental genotype distributions
flowchart LR
  A1[father] --> A3(couple)
  A2[mother] --> A3(couple)
  A3[couple] --> B("child
   genotype")
  A3[couple] --"genetic nurture"--> C("child
   environment")
  B("child
   genotype") --> D("child
    education")
  C("child
   environment") <--"gene×environ"--> B("child
    genotype")
  C("child
   environment") --> D("child
    education")
Figure 1: How parents affect child education outcomes

Estimation results

Controls used in estimation

  • 10 principal components of PGS
  • Parent-child age difference

Data: Minnesota Twin Study

  • Cognitive measures to estimate IQ
    • Wechsler Intelligence Scale for Children-Revised (WISC-R)
    • Wechsler Adult Intelligence Scale-Revised (WAIS-R)
  • Noncognitive measures
    • MPQ (Mulitdimensional Personality Questionnaire)
      • PA (positive emotionality of affectivity; well-being, social potency, achievement, social closeness)
      • NA (negative emotionality of affectivity; stress reaction, alienation, aggression)
      • constraint (control, harm avoidance, traditionalism)
    • DSM-IV (Diagnostic and Statisitcal Manual of Mental Disorders, fourth edition)
      • Externalizing: defiant disorder, conduct disorder, adult antisocial behavior
      • Academic effort: 8 items answered by twin mothers
      • Academic problems: 3 items answered by twin mothers
  • Family background
    • Hollingsworth scale on occupational status
    • Four year college degrees of parents

IGE

IGE
  • IGE = .13 is small relative to previous studies (.2 ~ .3)
    • Attenuation (measurement errors in family incomes)
    • European population has lower IGEs, Sweden = .125
    • Reduced by -482% when PGS and mediators are added
  • Effects of PGS
    • = .078 in (2)
    • = 0 in (3) when mediators of PGS are added

recursive SEM

recursive SEM

Education years↑ with

  • Cognitive ability, noncognitive ability
    • PGS of child, parents are not related when parental education, family income are added
  • Parental income, education
    • Impacts are twice as large for parental education

Cognitive ability↑ with

  • PGS

Noncognitive ability↑ with

  • PGS, smaller magnitude

recursive SEM

recursive SEM

Dizygotic twins (fraternal twins)

Education years↑ with

  • PGS of child and mother
    • PGS of father is unrelated
  • Parental income, education
    • Magnitude is larger for parental education

Parental education years↑ with

  • PGS of parents
    • Magnitude is larger for father PGS

Family income↑ with

  • PGS of parents
    • Magnitude is larger for father PGS

  • PGS of parents are not related to outcomes once IQ, soft skills index, parental education and family income are added
  • Most parental impacts on education are through incomes and parental education
  • No other indirect pathway remain from parental PGS, after parental education and incomes are addressed
    • No genetic nurture

感想

  • Multiple testing気にせず

References

Barth, Daniel, Nicholas W. Papageorge, and Kevin Thom. 2020. “Genetic Endowments and Wealth Inequality.” Journal of Political Economy 128 (4): 1474–1522. https://doi.org/10.1086/705415.
Becker, Gary S., and Nigel Tomes. 1979. “An Equilibrium Theory of the Distribution of Income and Intergenerational Mobility.” Journal of Political Economy 87 (6): 1153–89. https://doi.org/10.1086/260831.
Goldberger, Arthur S. 1989. “Economic and Mechanical Models of Intergenerational Transmission.” The American Economic Review 79 (3): 504–13. http://www.jstor.org/stable/1806859.
Lee, James J, Robbee Wedow, Aysu Okbay, Edward Kong, Omeed Maghzian, Meghan Zacher, Tuan Anh Nguyen-Viet, et al. 2018. “Gene Discovery and Polygenic Prediction from a Genome-Wide Association Study of Educational Attainment in 1.1 Million Individuals.” Nature Genetics 50 (8): 1112–21.
Okbay, Aysu, Jonathan P Beauchamp, Mark Alan Fontana, James J Lee, Tune H Pers, Cornelius A Rietveld, Patrick Turley, et al. 2016. “Genome-Wide Association Study Identifies 74 Loci Associated with Educational Attainment.” Nature 533 (7604): 539.

http://seiroito.github.io/RILM_PGSEdu_JPE2023.html